A problem in many dealerships is lack of good technical communication at times. The guy you talk to isn't a technician, he's a service writer and most of those guys were never techs or really know many technical details themselves YET they still have to at least try to sound as professional as possible. Some ask techs when they don't know while others will make up a story, trying to tell the customer what he thinks that customer wants to hear. That's what I think happened in your case with the SW story IMO.

What else could be happening? Although you might think it's trans related, it might be a fuel (driveabilty) problem instead, a possible problem with a MAF meter or ETM (throttle module) which are both common part failures with your mileage.
An experienced tech could determine that vs a trans problem. I'm speculating but you really need to have a dealer tech diagnose that.